Abstract— It has been shown that quasi orthogonal space time

block codes (QOSTBC) can achieve high transmission rate with

partial diversity. Constellation rotational QOSTBC can achieve

full diversity. In this paper, we present a constellation rotational

QOSTBC concatenates Reed–Solomon (RS) error correction

code structure. At the receiver, pairwise detection and error

correction are first implemented. The decoded data are

regrouped. Parallel interference cancellation (PIC) and dual

orthogonal space time block code (OSTBC) decoding are

deployed to the regrouped data. The dual OSTBC decoding can

obtain better error performance than constellation rotational

QOSTBC. The pure concatenated scheme is shown to have

higher diversity order and have better error performance at

high signal-to-noise ratio (S*R) scenario than both QOSTBC

and OSTBC schemes. The PIC and dual OSTBC decoding

algorithm can further obtain approximate 1.0 dB gains than

pure concatenated scheme at 10-6 bit error probability (BEP).

The BEP performance of the proposed algorithm is very close to

that of dual OSTBC scheme with perfect interference

cancellation.

Index Terms—OSTBC, QOSTBC, Constellation Rotation, RS

Code, Parallel Interference Cancellation

I. INTRODUCTION

UASI-ORTHOGONAL space-time block codes

(QOSTBC) have recently become an attractive topic

because it can achieve high transmission rate compared to

orthogonal space-time block code (OSTBC) by scarifying

partial diversity [1]. The outage performance upper bound is

derived for QOSTBC in [2]. The maximum-likelihood (ML)

decoder works with pairwise symbols for QOSTBC, thus its

decoding complexity increases exponentially. A low

complexity sphere decoding algorithm was put forward to

decouple pairwise symbols decoding into single symbol

decoding in [3]. J. Kim et. al proposed another efficient

decoding algorithm based on iterative interference

cancellation [4]. Besides some low complexity decoding

algorithms [5, 6], many works have been done to achieve

higher transmission rate or higher diversity. An improved

QOSTBC design can guarantee both full diversity and fast

ML decoding by choosing half of the symbols from a signal

Z. H. Yan is a Ph. D student in Shanghai Jiao Tong University, China and

with College of Information Science and Engineering, Henan University of

Technology, China. (e-mail:yanzhenghang@sjtu.org)

Y. H. Yang is with the Electrical Engineering Department, Shanghai Jiao

Tong University, China.

Y. L. Lu and M. D. Ma are with the School of Electrical and Electronic

Engineering, Nanyang Technological University.

constellation set and the other half of them from a rotated

constellation set [7, 8]. Using channel correct code and

parallel interference cancellation (PIC) is another approach

to achieve high throughput and good performance with low

complexity detection and decoding algorithm [9]. However,

the PIC algorithm in [9] needs enough receive antennas at

receiver like in Bell Labs Layered Space-Time (BLAST)

and Generalized Layered Space-Time (GLST) architectures

[10, 11].

In this letter, we propose a new PIC different from [9] for

QOSTBC transmitting. There is no limits for receive

antennas number. The optimal constellation rotation is used

for QOSTBC. Forward error correction (FEC) code is

introduced at transmitter. At receiver, the pairwise joint

detection is first used in our new method. After the error

correction process by FEC, we reconstruct the transmitting

constellation symbols and divide them into two groups.

When one group of signals are removed from the received

signals, the system is equivalent to dual OSTBC systems.

Then, linear ML decoding can be processed for the dual

OSTBC systems. Full diversity gain and FEC code gain can

be simultaneously obtained. Reed–Solomon (RS) error

correction codes [12] are used as FEC codes in this paper. RS

codes were put forward by Irving Reed and Gus Solomon in

the journal of the society for industrial and applied

mathematics [13]. These codes have great power and utility,

and are today found in a wide variety of commercial

applications such as CD, DVD and WiMAX. By using

different constellation sizes and different RS code rate, the

system can allow for a flexible choice of transmission rates.

The dual OSTBC decoding can obtain more gain than the

QOSTBC with constellation rotation. Numerical results

show that the concatenated theme can achieve higher

diversity order than both QOSTBC and OSTBC for the same

transmission rate and total transmission power constraint. At

high signal noise ratio (SNR) scenario, the bit error

probability (BEP) performance of the concatenated scheme

is far better than that of QOSTBC and OSTBC. The

proposed PIC and dual OSTBC decoding algorithm can

achieve about 1.0 dB gains than the concatenated scheme

without using PIC algorithms at high SNR scenarios, too.

The BEP performance of the proposed algorithm is very

close to that of dual OSTBC scheme with perfect

interference cancellation.

The organization of the paper is as follows. Section 2

provides a QOSTBC concatenated with RS error correction

code scheme. Section 3 derives the PIC and dual OSTBC ML

decoding algorithm for the proposed scheme. Simulation

An Improved Decoding for Constellation Rotation QOSTBC

Concatenates RS Code Using Interference Cancellation

Zhenghang Yan, Yuhang Yang, Maode Ma, IEEE Member, and Yilong Lu, IEEE Member

Q

QOSTBC

Encoder

2M-ary Constellation

Mapper & Interleaving

.

.

. NT

1RS Encoder 1S/P

RS Encoder NT

.

.

.

User Data

.

.

.

.

.

.

(a) Transmitter: QOSTBC concatenated RS code structure

QOSTBCJoint

DeCoding

2M-ary ConstellationDeMapper &

DeInterleaving

.

.

.

NR

1

RS Error Correct 1. . .

RS Error Correct NT

Regroup

PIC

PICDual OSTBC ML Decoding

Dual OSTBC ML Decoding

P/S

Output Data

.

.

.

...

(b) Receiver: PIC and dual OSTBC decoding

Fig. 1. Transmitter and receiver structures

results are presented in section 4 and conclusions are

summarized in section 5.

II. THE CONCATENATED QOSTBC SCHEME

We focus on the widely used QOSTBC scheme in [1] for

systems with four transmit antennas and nR receive antennas.

Analysis for other QOSTBCs and any transmit/receive

antennas is similar. Quasi-stationary flat Rayleigh fading

channel is assumed and ideal channel state information (CSI)

is available at the receiver. The proposed concatenated

QOSTBC structure is shown in Fig. 1a. Considering a 2M

-ary

constellation, the input data stream is demultiplexed into M

data substreams in series/parallel (S/P) convertor. Each

substream is encoded using a RS code respectively. The ith

bits

from all M RS codewords collectively select the ith

2M

-ary

constellation point si. Every 4L constellation symbols

compose one frame. After all 4L constellations symbols have

been decided in a frame, we take the lth

, the (l+L)th

, the

(l+2L)th

and the (l+3L)th

symbols (l=1,…,L) as a group and

denote them as x1(l), x2(l), x3(l), x4(l). Then, the QOSTBC

codewords transmitted at the lth

time slot are expressed as [1]

* *

1 2 3 4

* *12 34 2 1 4 3

* * * *34 12 3 4 1 2

* *

4 3 2 1

- -

- -

- -

T

x x x x

x x x x

x x x x

x x x x

= = −

A AΑ

A A

(1)

where * is conjugate operation and

* *

m n

mn

n m

x x

x x

= −

A (2)

The index l is ignored for simplify. For the elements in (1), x1

and x2 are selected from the constellation space А, x3 and x4

are selected from the constellation space ejθА. We call the

constellation space ejθA as space B. Let the total transmitted

energy across all nT transmit antennas be 1 for each time slot.

The received signal at the nR receive antennas is

TY = HΑ + * (3)

where received signal Y is an �R×4 matrix. The element

hij of the �R�T channel matrix H is the total channel

gain from the jth

transmit antenna to the ith

receive

antenna. * is an �R×4 noise matrix whose entries are

i.i.d complex Gaussian noise with mean 0 and variance σ2

n , and independent over time slots.

III. DETECTION AND DECODING

At the receiver, QOSTBC pairwise ML joint detection is first

applied to the received signals as shown in Fig. 1b. By

minimizing f14(x1, x4) the transmitted symbols x1 and x4 can be

decoded pairwise and the transmitted symbols x2 and x3 can be

decoded pairwise by minimizing f23(x2, x3) as [1, 7].

{ }

( ){(( )( ) }

1 4

1 4

1 1

1 4 14 1 4,

* * * *

1 1 2 2 3 3 4 4 1,

1

* * * *

4 1 3 2 2 3 1 4 4

2 2* * * * *

1 4 2 3 2 3 1 4 1 4 1 4

, min ( , )

min 2 Re

R

x x

�

m m m m m m m mx x

m

m m m m m m m m

m m m m m m m m F

x x f x x

h y h y h y h y x

h y h y h y h y x

h h h h h h h h x x x x

∈ ∈

∈ ∈=

=

= − − − −

+ − + + −

+ − − + + +

∑

Α B

Α B

H ( ))}2

(4)

and

{ }

( ){(( )( ) }

2 3

2 3

1 1

2 3 23 2 3,

* * * *

2 1 1 2 4 3 3 4 2,

1

* * * *

3 1 4 2 1 3 2 4 3

2* * * * *

2 3 1 4 1 4 2 3 2 3

, min ( , )

min 2 Re

R

x x

�

m m m m m m m mx x

m

m m m m m m m m

m m m m m m m m F

x x f x x

h y h y h y h y x

h y h y h y h y x

h h h h h h h h x x

∈ ∈

∈ ∈=

=

= − + − +

+ − − + +

+ − − + +

∑

Α B

Α B

H ( ))}2 2

2 3x x+

(5)

The simplified ML decoding algorithms in [3, 4] can be used

in place of the algorithm in [1] in order to reduce computation

complexity. After joint detection, 2M

-ary constellation

de-mapping, de-interleaving and RS error correction are

operated to the decoded data in a frame. After error correction

is completed, we take interleaving and 2M

-ary constellation

mapping process to the corrected data frame in the same way

as the process in the transmitting process and get x1

1 , x1

2 , x1

3 and

x1

4 , where superscript 1 denotes the 1th

iterative. The symbols x1

3 and x1

4 are input to a PIC module and the symbols x1

1 and x1

2

are input to another PIC module. At the first PIC module, we

remove x1

3 and x1

4 from the received signals by

1* 1

3 4

1* 1

4 31

12 1 1*

3 4

1 1*

4 3

0 0 -

0 0 - -

- 0 0

0 0

x x

x x

x x

x x

= −

Y Y H (6)

The subscript of Y1

12 indicates that the signals Y1

12 are

contributed by x1 and x2. The superscript of Y1

12 indicates

iterative number. Assuming x1

3 and x1

4 are successfully

decoded (x3= x1

3 and x4= x1

4 ), then

*

1 2

*

2 11

12 *

1 2

*

2 1

- 0 0

0 0

0 0 -

0 0

x x

x x

x x

x x

= +

Y H * (7-1)

or

5 10 15 20 25 30 3510

-6

10-5

10-4

10-3

10-2

10-1

SNR (dB)

Bit Error Porbability

2 bits/s/Hz

Uncoded

OSTBC

QOSTBC

Rotation QOSTBC

Rot QOSTBC + RS

Rot QOSTBC+RS+PIC

RS+PIC Bound

Fig. 2. Bit-error probability versus SNR for all transmission schemes at 2 bits/sec/Hz; 4 transmit antennas, 1 receive antenna

[ ] [ ]* *

1 2 1 21

12 3 4* *

2 1 2 1

- -

x x x x

x x x x

= +

1 2Y h h h h * (7-2)

where hi is the ith

column vector of channel matrix H.

Obviously, there are two independent OSTBC received

signals in (7-2). We derive the decision metric

2*

1 2

*

2 11

12 *

1 2

*

2 1

- 0 0

0 0

0 0 -

0 0 F

s s

s s

s s

s s

−

Y H (8)

where ||.||2

F is squared Frobenius norm, s1 and s2 are all possible

transmitting constellation symbols. Minimizing the decision

metric results in a ML decoding. We expand the above metric

and get two independent parts, one of which is only a function

of s1 and the other one is only a function of s2. Thus, after

some manipulation x1 can be detected by minimizing the

decision metric

( ) ( )( )

( ) ( )( )

2

1 * 1 * *

12 3 12 4 1

1

24

2 21 * 1 *

12 1 12 2 1 1

1 1 1

,3 ,4

,1 ,2 2

R

R R

�

j j

j

� �

j j ji

j j i

y j h y j h s

y j h y j h s h s

=

= = =

+ − +

+ − + − +

∑

∑ ∑∑

(9)

and x2 can be detected by minimizing the decision metric

( ) ( )( )

( ) ( )( )

2

1 * 1 * *

12 4 12 3 2

1

24

2 21 * 1 *

12 2 12 1 2 2

1 1 1

,3 ,4

,1 ,2 2

R

R R

�

j j

j

� �

j j ji

j j i

y j h y j h s

y j h y j h s h s

=

= = =

− − +

− − + − +

∑

∑ ∑∑

(10)

where y1

12(j,i) is the jth

row, the ith

column element of Y1

12. It is

shown that x1 and x2 can be solely detected with linear ML

decoding algorithm respectively. At high SNR, the error

performance of dual OSTBC decoding is superior to that of

the QOSTBC with constellation rotation because the

interference is cancelled from the received signals.

Comparing with pariwise detection, the increased

computation of solely detection is also accepted. Similarly,

x3 and x4 can be detected in the same way in another PIC and

dual OSTBC ML decoding branch.

The detected x1, x2, x3 and x4 are input to 2M

-ary

constellation de-mapper and are dealt with the same process

after QOSTBC joint detection. The user data can be obtained

at the output of parallel/serial convertor. Furthermore, the

PIC and dual OSTBC decoding process can be iteratively

implemented after x1, x2, x3 and x4 are all decoded as shown

in Fig.1b.

IV. NUMERICAL RESULTS

In this section, we provide simulation results for the

proposed PIC and dual OSTBC decoding algorithm and

compare it with the results for other transmitter/receiver

schemes. In all simulations, four transmit antennas and one

receive antenna are deployed similarly as in [1]. The total

average transmission power keeps constant for all schemes.

Fig.2 provides simulation results for the transmission rate of

2 bits/s/Hz. In order to keep the same transmission rate, we

used appropriate constellation size for different transmission

schemes. QPSK is used for uncoded scheme and rate one

QOSTBC. 16-QAM is adopted for the proposed concatenated

scheme and rate ½ OSTBC. The optimal rotation angle θ=π/4

is adopted for constellation rotation QOSTBC with QPSK and

16-QAM modulation [8]. There is no rate ½ RS code, thus we

obtain rate ½ by using three 7/15 RS code blocks and one 9/15

BCH code block as one transmission unit.

The slope of the BEP-SNR curve dictates the degree of

diversity. Constellation rotation QOSTBC achieves as full

diversity as OSTBC and its error performance is superior to

OSTBC and QOSTBC. Fig.2 shows that the scheme using

QOSTBC concatenated RS code has higher diversity order

than full diversity order because FEC code gains are

introduced. At very low SNR, concatenated scheme has bad

error performance because large constellation size is adopted.

The error performance of the concatenated scheme is better

than constellation rotation QOSTBC when SNR>16.3 dB and

obtains 3.5 dB gain at 10-6

BEP. The proposed PIC and dual

OSTBC decoding scheme can achieve full diversity order and

FEC code gain simultaneously. Comparing with pure

concatenated scheme, the proposed PIC algorithm only

obtains a little gain at very low SNR scenario. The reason lies

in that in some frames decoding errors are beyond the

correction capability of RS code and more errors are incurred

after error correction process on the contrary. The proposed

PIC scheme can obtain obvious gain than pure concatenated

scheme except at very low SNR scenario. For example, 1.0 dB

gains are obtained at 10-6

BEP. The performance upper bound

of the proposed PIC scheme is also described in Fig.2. It is

assumed that perfect PIC is implemented for performance

upper bound. The distance between performance upper bound

and BER curve of the proposed PIC scheme is about 0.4 dB. It

is introduced by decoding errors at pairwise ML decoding and

error propagation in PIC process. Numerical outcome shows

that no gain is obtained at the second iterative PIC process and

the BEP curve of the second iterative PIC process is ignored

in this paper. It is because RS code is a kind of block code and

iterative decoding can not improve the performance of block

code.

V. CONCLUSIONS

We have deployed a constellation rotational QOSTBC

concatenated RS error correction code structure at the

transmitter. At the receiver, after pairewise ML detection and

error correction, the proposed PIC and dual OSTBC detection

are used. In the proposed PIC scheme, rate one is fulfilled for

QOSTBC. Full diversity is achieved by dual OSTBC ML

decoding after PIC is implemented. Code gain is obtained by

using RS error correction code. Thus, full transmitting rate,

full diversity and FEC code gain can be obtained

simultaneously. The constellation rotational QOSTBC

concatenated RS code structure have better BEP performance

than QOSTBC and OSTBC schemes except at very low SNR

scenario. The proposed PIC and dual OSTBC decoding

algorithm for the concatenation scheme can provide about 1.0

dB performance gains at 10-6

BEP. After PIC and dual

OSTBC ML decoding, the BEP performance of the

concatenated QOSTBC scheme is very close to that of dual

OSTBC scheme.

ACKNOWLEDGMENT

The authors would like appreciate Chinese Scholarship

Council for the financial support.

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